/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 284 Solve. $$ 4 b^{2}+7 b=-3 $... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 284

Solve. $$ 4 b^{2}+7 b=-3 $$

Short Answer

Expert verified
-\( \frac{3}{4} \) or -1

Step by step solution

01

- Write the equation in standard quadratic form

To solve the quadratic equation, start by moving all terms to one side so that the equation is in the form of \[ax^2 + bx + c = 0\]. In this case, add 3 to both sides to get: \[4b^2 + 7b + 3 = 0\].
02

- Identify coefficients

Identify the coefficients in the quadratic equation \[4b^2 + 7b + 3 = 0\]. Here, a = 4, b = 7, and c = 3.
03

- Use the quadratic formula

Apply the quadratic formula \[b = \frac{-B \pm \sqrt{B^2 - 4AC}}{2A}\] where A = 4, B = 7, and C = 3. Substitute these values into the formula: \[b = \frac{-7 \pm \sqrt{7^2 - 4 \cdot 4 \cdot 3}}{2 \cdot 4}\].
04

- Simplify under the square root

Calculate inside the square root: \[7^2 - 4(4)(3) = 49 - 48 = 1\]. So the equation becomes: \[b = \frac{-7 \pm \sqrt{1}}{8}\].
05

- Solve for b

Simplify the equation further. Since \(\sqrt{1} = 1\), we get: \[b = \frac{-7 \pm 1}{8}\]. Solve for each case: \[b = \frac{-7 + 1}{8} = \frac{-6}{8} = -\frac{3}{4}\] and \[b = \frac{-7 - 1}{8} = \frac{-8}{8} = -1\].

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Quadratic Formula
The quadratic formula is a powerful tool for solving quadratic equations. A quadratic equation is any equation that can be written in the form \(ax^2 + bx + c = 0\). This formula provides the solutions to the equation without needing to factor it. The quadratic formula is given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\].

Here鈥檚 what each part of the formula means:
  • \

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In the following exercises, factor each expression using any method. $$ 12 y^{2}-29 y+14 $$

In the following exercises, factor each trinomial of the form \(x^{2}+b x y+c y^{2} .\) $$ p^{2}-2 p q-35 q^{2} $$

In the following exercises, factor each trinomial of the form \(x^{2}+b x y+c y^{2} .\) $$ x^{2}-3 x y-14 y^{2} $$

In the following exercises, factor completely using trial and error. $$ 6 y^{4}+12 y^{3}-48 y^{2} $$

In the following exercises, factor each trinomial of the form \(x^{2}+b x+c .\) $$ n^{2}+19 n+48 $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.